Abstract. The present paper is devoted to the derivation of an explicit form of linearly representable random fields in the form
where , is a Hilbert space, operators are such that and where
.

The results obtained are the generalization of theorem proved in [3], [5], [7].

It is shown that a rank of nonstationary of field
depends
not only on a degree of non-self adjoint of but on a degree of
nilpotency of commutator .

In the present paper an explicit form of correlation function for discrete
spectrum of and is derived. A form in the case of spectrum of operator is constructed in zero and that of the operator
is pure discrete
of
and is zero and the other is discrete, is obtained.